Stone buildings are a whole different beast compared to timber frames — the thermal mass works for you in summer but absolutely against you when you're trying to heat a cold space quickly in winter.
First question: are you planning occasional use or living in it regularly? That completely changes the approach.
For occasional use, you honestly might be better off with internal insulated stud walls (losing a bit of floor space but keeping your heating bills sane). Rigid PIR boards like Kingspan or Celotex battened out from the stone gives you decent U-values without going too deep. Don't forget the floor — cold stone floors will absolutely murder your heat retention and people ignore them constantly.
Moisture is the elephant in the room with old stone though. A lot of traditional stone buildings breathe, and if you slap vapour barriers everywhere you can end up with damp trapped in the wall causing all sorts of problems. Worth understanding whether your building is lime-mortared or cement-pointed before making any decisions — they behave completely differently.
Roof is usually where you lose most heat so I'd prioritise that first if budget is tight.
What's your current heating plan? That'll affect insulation spec too — if you're going wood burner you can get away with less, but if you're running electric (especially off-grid where every watt counts), you need to be much more aggressive with the spec.
Plenty of people on here have done exactly this — hopefully a few will chip in with what worked and what didn't. Stone outbuilding conversions seem to be very much a regional thing as well, so where in the country are you?